Banach space theory : the basis for linear and nonlinear analysis / Marian Fabian, Petr Habala, Petr Hajek,... [et al.]

The book is a substantial text (over 800 pages long) that combines an introduction to the basic principles of functional analysis with more advanced topics that lead the reader to many frontiers of current research in Banach spaces. From the Preface of the book: “ ...It is the purpose of this introductory text to help the reader grasp the basic principles of Banach space theory and nonlinear geometric analysis.

The text presents the basic principles and techniques that form the core of the theory. It is organized to help the reader proceed from the elementary part of the subject to more recent developments. ...Experience shows that working through a large number of exercises, provided with hints that direct the reader, is one of the most efficient ways to master the subject. Exercises are of several levels of difficulty, ranging from simple exercises to important results or examples. They illustrate delicate points in the theory and introduce the reader to additional lines of research. ...

An effort has been made to ensure that the book can serve experts in related fields such as Optimization, Partial Differential Equations, Fixed Point Theory, Real Analysis, Topology, and Applied Mathematics, among others.

As a prerequisite, basic undergraduate courses in calculus, linear algebra, and general topology, should suffice.” ... (zbMath)